Dynamic phase transition of the globally-coupled kinetic Ising model in the low-frequency region

We revisit the globally-coupled kinetic Ising model in the presence of an oscillating external magnetic field with an amplitude h₀ and a driving angular frequency ω. In the low-frequency region ω → 0, the dynamic phase transition is shown to become discontinuous, and the phase boundary is found to be described by h₀ ̃ (1 - T)^3/2 with the temperature T and a critical temperature of unity in the limit h ₀ → 0. Our result is complementary to h₀ ̃ (1 - T)^1/2, previously known for the other limit (1 - T) « ω. We extend the existing analytic calculation for the continuous transition to the second-order perturbation expansion and find that the dynamic phase transition occurs at lower temperature than the static one, which was not captured by the existing first-order calculation. The stochastic resonance behavior is also discussed in relation to the nature of the dynamic phase transition.